A categorical K\"unneth formula for constructible Weil sheaves

TL;DR

This paper establishes a K"unneth formula for derived categories of constructible Weil sheaves on schemes in characteristic p, extending to various coefficients and applications to moduli stacks of shtukas.

Contribution

It proves a K"unneth-type equivalence for derived categories of Weil sheaves with new coefficients and applies it to moduli stacks of shtukas.

Findings

K"unneth equivalence for Weil sheaves established

Extension to various coefficient rings including finite and algebraic extensions

Application to cohomology of moduli stacks of shtukas

Abstract

We prove a K\"unneth-type equivalence of derived categories of lisse and constructible Weil sheaves on schemes in characteristic $p > 0$ for various coefficients, including finite discrete rings, algebraic field extensions $E \supset \mathbf Q_\ell$, $\ell \ne p$ and their rings of integers $O_E$. We also consider a variant for ind-construtible sheaves which applies to the cohomology of moduli stacks of shtukas over global function fields.